Problem: Solve for $x$ and $y$ using elimination. ${-x-6y = -23}$ ${x-5y = -10}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-11y = -33$ $\dfrac{-11y}{{-11}} = \dfrac{-33}{{-11}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {-x-6y = -23}\thinspace$ to find $x$ ${-x - 6}{(3)}{= -23}$ $-x-18 = -23$ $-x-18{+18} = -23{+18}$ $-x = -5$ $\dfrac{-x}{{-1}} = \dfrac{-5}{{-1}}$ ${x = 5}$ You can also plug ${y = 3}$ into $\thinspace {x-5y = -10}\thinspace$ and get the same answer for $x$ : ${x - 5}{(3)}{= -10}$ ${x = 5}$